I.T. Todorov
Two--Dimensional Conformal Field Theory and Beyond. Lessons from a Continuing Fashion
Preprint series: ESI preprints

MSC:

46N50 Applications in quantum physics

81T05 Axiomatic quantum field theory; operator algebras

81T30 String and superstring theories; other extended objects , See also {83E30}

Abstract: Two-dimensional conformal field theory (CFT) has several sources:
the search for simple examples of quantum field theory, the
description of surface critical phenomena, the study of
(super)string vacua.

In the present overview of the subject we emphasize the role of
CFT in bridging the gap between mathematics and quantum field
theory and discuss some new physical concepts that emerged in the
study of CFT models: anomalous dimensions, rational CFT, braid
group statistics.

In an aside, at the end of the paper, we share the misgivings,
recently expressed by Penrose, about some dominant trends in
fundamental theoretical physics.

Keywords: quantum field theory, conformal field theory, anomalous dimensions, braid group statistics